Hertz Contact Stress

Using Hertz contact formula I calculated contact stress for cylinder in contact with cylinderical socket but I dont know to which stress to compare this contact stress.Actally I comapred with material bearing stress & calculated stress was less that bearing stress(got margin of saftey 2), but I am not sure whether to comapre this with the baering stress so please some body tell me to which allowable stress to compare this contact stress.

Well to calculate the Hertz conatact stress i used the folowing formula.

stress=.591*SQRT(p*E/Kd)

And if I want to compare hertz stress with shear stress what wold be the relation between two.

The concern with contact stresses like this is that they are usually cyclic and thus you don't run into the typical tensile test failure modes. Whenever we talk about Hertz stresses like this, we are usually looking at our bearings. In these cases, the loading is such that crack formation is usually the main concern. To top it all off, if you ever get a chance to look at some of the theory, if you take two spheres and load them, the contact pressure is not the highest stress to be found. The higher stress levels are below the surface. This makes crack detection a lot tougher because it necessitates x-ray inspection.

As a starting point, if you really want to have a number to compare against, I would start with the max shear stress as a comparison. Again though, you do have other areas you need to address as well. Good luck.

yeah, before you use anything to make a conclusion you really need to think about what you're trying to accomplish. Contact problems usually involved a whole lot more than a single quasi-static loading of a simple geometry (like if the word 'wear' comes up the situation can become really complex). But if you're after just seeing how you situation generally 'is' with respect to yield, using typically yield conditions (von Mises stress and alike) is one way to go (and perhaps the first). In a specific application a lot can be said from the value of the contact pressure itself (using engineering tools and methods for that application assuming a certain pre-existing situation). Just make sure if you're actually trying to get to the failure of the surface you don't take too simplistic of an approach (take a look at any tribology/wear book and the number of mechanisms for surface failure and what different issues affect them ---> lots of different criteria and models utilizing different measures of stress, deformation, material properties etc).

I think have seen somewhere along with contact pressure solutions tables/simplified formula for under the contact shear stresses (along with at the edge of contact tensile stress). Such might be usable in this case if want to get results without dwelling on the problem too much (simplified that is). Not sure if Roark having a basic collection of Hertz cases has anything such though, don't think too extensively at least (might be that am remembering some articles and such).